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17 Jul 2019, 00:22
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
79% (02:39) correct
21%
(02:57)
wrong
based on 276
sessions
History
Date
Time
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Not Attempted Yet
At 9 am train X left from station A towards station B at uniform speed of 90km/hr. After 2 hours another train Y leaves from station B on a parallel track towards station A at uniform speed of 60km/hr. If train X reached station B at 2 pm, at what time will the two train cross each other?
(A) 10 : 12 am
(B) 10 : 48 am
(C) 11 : 20 am
(D) 12 : 48 am
(E) 1 : 20 pm
(A) 10 : 12 am
(B) 10 : 48 am
(C) 11 : 20 am
(D) 12 : 48 am
(E) 1 : 20 pm
firas92
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Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 616
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
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17 Jul 2019, 00:30
Kudos
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Train X completed the journey from A to B in 5 hours. So the distance between A and B is 90*5 = 450 miles
In 2 hours, Train X travels 180 miles. So when Train Y starts, the distance between X and Y is 450-180=270 miles
Since the trains are travelling towards each other, their relative speed is 90+60 = 150 miles/hour
So they meet at \(\frac{270}{150}\) hours which is \(1\frac{4}{5}\) hours or 1 hour and 48 minutes after train Y starts (Train Y started at 11:00am)
So they meet at 12:48pm
Answer is (D)
In 2 hours, Train X travels 180 miles. So when Train Y starts, the distance between X and Y is 450-180=270 miles
Since the trains are travelling towards each other, their relative speed is 90+60 = 150 miles/hour
So they meet at \(\frac{270}{150}\) hours which is \(1\frac{4}{5}\) hours or 1 hour and 48 minutes after train Y starts (Train Y started at 11:00am)
So they meet at 12:48pm
Answer is (D)
General Discussion
17 Jul 2019, 00:44
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Bunuel
Concept used behind this problem is that when the two trains cross each other, the time taken to travel that distance for both the trains should be equal.
So, Train X reaches "B" at 2pm, thus total travel time for Train X is 5 hours. (as it leaves at 9am)
Thus total distance between A and B is = 90 km/hr x 5hrs= 450 kms.
Train Y leaves at 11am (after 2hrs).
Let the total distance travelled by train X upto the meeting point be \(x\) kms
Thus distance travelled by train Y is = \(450-x\)
Equating the time taken by both the trains to reach the meeting point:
\(\frac{x}{90} = 2 + \frac{(450-x)}{60}\) {as Train Y left after 2hours}
Solving for \(x\), we get \(x\)=342 kms
so time taken to reach meeting point by train X= \(\frac{342}{90}\) = 3.8 hrs
and as train X left at 9am, 3.8 hrs = 12:48 pm.
Answer is D
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